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Waht is the significance of even versus un even carbon distribution???
Heavy clumped up deposits on one side of the plug could mean oil deposits from a valve guide. When the plug is in place in the head, the side with the heavy deposits would be facing the leaking valve.
A more smooth even distribution would likely suggest carbon from fuel.
In your case, if the deposits are even and only on one cylinder, I would try replacing the spark plug wire and spark plug.
That would be the simplest thing to try and also the cheapest. Simple things are not always obvious.